Manuals/calci/MANNWHITNEYUTEST

MANNWHITNEYUTEST(xRange,yRange,Confidencelevel,Logicalvalue,Testtype)

• $xRange$ is the array of x values.
• $yRange$ is the array of y values.
• $Confidencelevel$ is the value between 0 and 1.
• $Logicalvalue$ is either TRUE or FALSE.
• $Testtype$ is the type of the test.

Description

• This function gives the test statistic value of the Mann Whitey U test.
• It is one type of Non parametric test.It is also called Mann–Whitney–Wilcoxon,Wilcoxon rank-sum test or Wilcoxon–Mann–Whitney test.
• Using this test we can analyze rank-ordered data.
• This test is alternative to the independent-sample, Student t test, and yields results identical to those obtained from the Wilcoxon Two Independent Samples Test.
• This test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
• Mann whitey u test is having the following properties:
• 1.Data points should be independent from each other.
• 2.Data do not have to be normal and variances do not have to be equal.
• 3.All individuals must be selected at random from the population.
• 4.All individuals must have equal chance of being selected.
• 5.Sample sizes should be as equal as possible but for some differences are allowed.
• Suppose the two groups of the populations have distributions with the same shape it can be viewed as a comparison of two medians.With out the assumption the Mann-Whitney test does not compare medians.
• To find statistic value of this test the steps are required:
  • 1.For the two observations of values, find the rank all together.
  • 2.Add up all the ranks in a first observation.
  • 3.Add up all the ranks in a second group.
  • 4.Select the larger rank.
  • 5.Calculate the number of participants,number of people in each group.
  • 6.Calculate the test statistic:$U={\frac {n_{1}*n_{2}+nx(nx+1)}{2-Tx}}$
• where $n_{1}$ and $n_{2}$ are number of participants and number of people.
• $Tx$ is the larger rank total.$nx$ is the similar value of $n1$.
  • 7.State Result: In this step we have to take a decision of null hypothesis either accept or reject depending on the z value using critical value table.
  • 8.State Conclusion: To be significant, our obtained U has to be equal to or LESS than this critical value.

Example

X	Y
87	71
72	42
94	69
49	97
56	78
88	84
74	57
61	64
80	78
52	73
75	85
0	91

1. =MANNWHITNEYUTEST(A1:A12,B1:B13,0.05,true)

Mann Whitney U Test Ranks

X	Y
19	9
10	1
22	8
2	23
4	14.5
20	17
12	5
6	7
16	14.5
3	11
13	18
0	21

Ranks	127	149
Median	74	75.5
n	11	12

RESULTS

U1	71
U2	61
U	61
E(U1)	132
E(U2)	144
E(U)	66
StdDev	16.24807680927192
a	0.05
z	-0.3077287274483318
p	0.7582891742833224